Ideal Criteria for both Ideal Criteria for both X2-dy2 = M1 And X2-dy2 = M2 to have Primitive Solutions for any Integers M1, M2 Prime to D > 0

This article provides necessary and sufficient conditions for both of the Diophantine equations X^2 − DY^2 = m1 and x^2 − Dy^2 = m2 to have primitive solutions when m1 , m2 ∈ Z, and D ∈ N is not a perfect square. This is given in terms of the ideal theory of the underlying real quadratic order Z[√D].

On a Class of Vertex Folkman Numbers

Let a1 , . . . , ar, be positive integers, i=1 ... r, m = ∑(ai − 1) + 1 and p = max{a1 , . . . , ar }. For a graph G the symbol G → (a1 , . . . , ar ) means that in every r-coloring of the vertices of G there exists a monochromatic ai -clique of color i for some i ∈ {1, . . . , r}. In this paper we consider the vertex Folkman numbers F (a1 , . . . , ar ; m − 1) = min |V (G)| : G → (a1 , . . . , ar ) and Km−1 ⊂ G} We prove that F (a1 , . . . , ar ; m − 1) = m + 6, if p = 3 and m ≧ 6 (Theorem 3) and F (a1 , . . . , ar ; m − 1) = m + 7, if p = 4 and m ≧ 6 (Theorem 4).

Generalizations of Cole's Systems

There are four resolvable Steiner triple systems on fifteen elements. Some generalizations of these systems are presented here.

Search for Wieferich Primes through the use of Periodic Binary Strings

The result of the distributed computing projectWieferich@Home is presented: the binary periodic numbers of bit pseudo-length j ≤ 3500 obtained by replication of a bit string of bit pseudo-length k ≤ 24 and increased by one are Wieferich primes only for the cases of 1092 or 3510.

Finite Groups as the Union of Proper Subgroups

2000 Mathematics Subject Classification: 20D60,20E15.

On the Vertex Folkman Numbers Fv(2,...,2;q)

2000 Mathematics Subject Classification: 05C55.

Class Number Two for Real Quadratic Fields of Richaud-Degert Type

2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.

Using a Bilingual Reading Strategy to Reduce SLD Numbers

Studies show that for Spanish speaking students, vocabulary expansion in Spanish increases fluency and comprehension in English. Therefore, creating a bilingual reading intervention program with a strong emphasis on vocabulary building in the early grades will help improve the students’ overall reading comprehension in English and avoid improper placement.

Political strategy, leadership, and policy entrepreneurship in Japanese defense policy and politics: A comparison of three prime ministerships

Since the end of the Cold War, Japan's defense policy and politics has gone through significant changes. Throughout the post cold war period, US-Japan alliance managers, politicians with differing visions and preferences, scholars, think tanks, and the actions of foreign governments have all played significant roles in influencing these changes. Along with these actors, the Japanese prime minister has played an important, if sometimes subtle, role in the realm of defense policy and politics. Japanese prime ministers, though significantly weaker than many heads of state, nevertheless play an important role in policy by empowering different actors (bureaucratic actors, independent commissions, or civil actors), through personal diplomacy, through agenda-setting, and through symbolic acts of state. The power of the prime minister to influence policy processes, however, has frequently varied by prime minister. My dissertation investigates how different political strategies and entrepreneurial insights by the prime minister have influenced defense policy and politics since the end of the Cold War. In addition, it seeks to explain how the quality of political strategy and entrepreneurial insight employed by different prime ministers was important in the success of different approaches to defense. My dissertation employs a comparative case study approach to examine how different prime ministerial strategies have mattered in the realm of Japanese defense policy and politics. Three prime ministers have been chosen: Prime Minister Hashimoto Ryutaro (1996-1998); Prime Minister Koizumi Junichiro (2001-2006); and Prime Minister Hatoyama Yukio (2009-2010). These prime ministers have been chosen to provide maximum contrast on issues of policy preference, cabinet management, choice of partners, and overall strategy. As my dissertation finds, the quality of political strategy has been an important aspect of Japan's defense transformation. Successful strategies have frequently used the knowledge and accumulated personal networks of bureaucrats, supplemented bureaucratic initiatives with top-down personal diplomacy, and used a revitalized US-Japan strategic relationship as a political resource for a stronger prime ministership. Though alternative approaches, such as those that have looked to displace the influence of bureaucrats and the US in defense policy, have been less successful, this dissertation also finds theoretical evidence that alternatives may exist.

(Table 1) Individual codes, haplotype codes, GenBank accession numbers for DNA sequences and sample locality of the analysed Betamorpha fusiformis specimens from the ANDEEP III expedition

Based on our current knowledge about population genetics, phylogeography and speciation, we begin to understand that the deep sea harbours more species than suggested in the past. Deep-sea soft-sediment environment in particular hosts a diverse and highly endemic invertebrate fauna. Very little is known about evolutionary processes that generate this remarkable species richness, the genetic variability and spatial distribution of deep-sea animals. In this study, phylogeographic patterns and the genetic variability among eight populations of the abundant and widespread deep-sea isopod morphospecies Betamorpha fusiformis [Barnard, K.H., 1920. Contributions to the crustacean fauna of South Africa. 6. Further additions to the list of marine isopods. Annals of the South African Museum 17, 319-438] were examined. A fragment of the mitochondrial 16S rRNA gene of 50 specimens and the complete nuclear 18S rRNA gene of 7 specimens were sequenced. The molecular data reveal high levels of genetic variability of both genes between populations, giving evidence for distinct monophyletic groups of haplotypes with average p-distances ranging from 0.0470 to 0.1440 (d-distances: 0.0592-0.2850) of the 16S rDNA, and 18S rDNA p-distances ranging between 0.0032 and 0.0174 (d-distances: 0.0033-0.0195). Intermediate values are absent. Our results show that widely distributed benthic deep-sea organisms of a homogeneous phenotype can be differentiated into genetically highly divergent populations. Sympatry of some genotypes indicates the existence of cryptic speciation. Flocks of closely related but genetically distinct species probably exist in other widespread benthic deep-sea asellotes and other Peracarida. Based on existing data we hypothesize that many widespread morphospecies are complexes of cryptic biological species (patchwork hypothesis).

(Tables 1, 3) Details of Agassiz trawl stations and numbers of specimens per macro- and megazoobenthic taxon collected during POLARSTERN cruise ANT-XXII/3 (ANDEEP III)

The assemblages inhabiting the continental shelf around Antarctica are known to be very patchy, in large part due to deep iceberg impacts. The present study shows that richness and abundance of much deeper benthos, at slope and abyssal depths, also vary greatly in the Southern and South Atlantic oceans. On the ANDEEP III expedition, we deployed 16 Agassiz trawls to sample the zoobenthos at depths from 1055 to 4930 m across the northern Weddell Sea and two South Atlantic basins. A total of 5933 specimens, belonging to 44 higher taxonomic groups, were collected. Overall the most frequent taxa were Ophiuroidea, Bivalvia, Polychaeta and Asteroidea, and the most abundant taxa were Malacostraca, Polychaeta and Bivalvia. Species richness per station varied from 6 to 148. The taxonomic composition of assemblages, based on relative taxon richness, varied considerably between sites but showed no relation to depth. The former three most abundant taxa accounted for 10-30% each of all taxa present. Standardised abundances based on trawl catches varied between 1 and 252 individuals per 1000 m2. Abundance significantly decreased with increasing depth, and assemblages showed high patchiness in their distribution. Cluster analysis based on relative abundance showed changes of community structure that were not linked to depth, area, sediment grain size or temperature. Generally abundances of zoobenthos in the abyssal Weddell Sea are lower than shelf abundances by several orders of magnitude.

Seawater carbonate chemistry and cell numbers during experiments with dinoflagellates, 2007

The effects of dissolved inorganic carbon (DIC) on the growth of 3 red-tide dinoflagellates (Ceratium lineatum, Heterocapsa triquetra and Prorocentrum minimum) were studied at pH 8.0 and at higher pH levels, depending upon the pH tolerance of the individual species. The higher pH levels chosen for experiments were 8.55 for C. lineatum and 9.2 for the other 2 species. At pH 8.0, which approximates the pH found in the open sea, the maximum growth in all species was maintained until the total DIC concentration was reduced below ~0.4 and 0.2 mM for C. lineatum and the other 2 species, respectively. Growth compensation points (concentration of inorganic carbon needed for maintenance of cells) were reached at ~0.18 and 0.05 mM DIC for C. lineatum and the other 2 species, respectively. At higher pH levels, maximum growth rates were lower compared to growth at pH 8, even at very high DIC concentrations, indicating a direct pH effect on growth. Moreover, the concentration of bio-available inorganic carbon (CO2 + HCO3-) required for maintenance as well as the half-saturation constants were increased considerably at high pH compared to pH 8.0. Experiments with pH-drift were carried out at initial concentrations of 2.4 and 1.2 mM DIC to test whether pH or DIC was the main limiting factor at a natural range of DIC. Independent of the initial DIC concentrations, growth rates were similar in both incubations until pH had increased considerably. The results of this study demonstrated that growth of the 3 species was mainly limited by pH, while inorganic carbon limitation played a minor role only at very high pH levels and low initial DIC concentrations.

What's in the Numbers? Child Welfare Statistics and the Children (NI) Order

This article draws attention to the importance of routinely collected administrative data as an important source for understanding the characteristics of the Northern Ireland child welfare system as it has developed since the Children (Northern Ireland) Order 1995 became its legislative base. The article argues that the availability of such data is a strength of the Northern Ireland child welfare system and urges local politicians, lobbyists, researchers, policy-makers, operational managers, practitioners and service user groups to make more use of them. The main sources of administrative data are identified. Illustration of how these can be used to understand and to ask questions about the system is provided by considering some of the trends since the Children Order was enacted. The “protection” principle of the Children Order provides the focus for the illustration. The statistical trends considered relate to child protection referrals, investigations and registrations and to children and young people looked after under a range of court orders available to ensure their protection and well-being.